Theorem orim2d 789

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 787	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  790  orbi2d  791  pm2.82  813  stdcndcOLD  847  pm2.13dc  886  exmid1dc  4243  acexmidlemcase  5938  poxp  6317  fodjuomnilemdc  7245  omniwomnimkv  7268  exmidontriimlem1  7332  indpi  7454  suplocexprlemloc  7833  nneoor  9474  uzp1  9681  maxabslemlub  11460  xrmaxiflemlub  11501  nninfctlemfo  12303  exmidunben  12739  bj-nn0suc  15833  sbthomlem  15897